AP Calculus ABmediummcq1 pt

If f(x)=x2exf(x)=\dfrac{x^2}{e^x}, then f(x)=f'(x)=

A.x(2x)ex\dfrac{x(2-x)}{e^x}
B.x22xex\dfrac{x^2-2x}{e^x}
C.2xex\dfrac{2x}{e^x}
D.x(2x)e2x\dfrac{x(2-x)}{e^{2x}}

Explanation

Core Concept

The quotient rule gives 2xexx2exe2x=2xx2ex\dfrac{2xe^x-x^2e^x}{e^{2x}}=\dfrac{2x-x^2}{e^x}. Factoring the numerator gives x(2x)ex\dfrac{x(2-x)}{e^x}.

Correct Answer

Ax(2x)ex\dfrac{x(2-x)}{e^x}

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